Today, let's cut the earth down to size. The
University of Houston's College of Engineering
presents this series about the machines that make
our civilization run, and the people whose
ingenuity created them.

Columbus sailed off, with
one part courage and two parts madness, to sail
around a spherical world. Actually, his trip was
based on a terrible miscalculation. He
underestimated earth's diameter, and he
overestimated the width of Asia. He thought Japan
lay only 2700 miles west of the Canary Islands. A
correct calculation would've put it 10,000 miles
away -- far beyond the reach of any 15th-century
ship. And yet Columbus had access to a much better
estimate of earth's size -- one that was 1700 years
old.

The ancients thought the earth was flat, but then
so did you and I when we were too young to know
about spheres. Understanding a round earth came in
stages. First the Pythagoreans argued by induction,
2500 years ago: The moon is round, they said. So is
the sun. Surely the earth must also be round.

Two centuries later, Aristotle argued from
observation. When a boat sails off in any
direction, he noted, its hull always disappears
before its sails do. The hull is obviously being
obscured by curvature, so the earth must be round.

Science writer John Noble Wilford notes that going
from flat to round meant carving earth down from
indefinitely large to a much more confined place.
The longest journey on a round earth will sooner or
later take you back where you began. The round
earth had somehow been made into something less
than the flat earth was, but how much less?
Educated people knew the earth was round in the 3rd
century BC, but they still didn't know how to
measure its size.

Then the Egyptian Eratosthenes, director of the
Library in Alexandria, wedded observation to
calculation. His idea was as simple as it was
brilliant. When the sun was directly above Aswan,
500 miles away, he measured the shadow cast by a
vertical tower in Alexandria. The rest was simple
trigonometry. He calculated earth's diameter with
only 16 percent error, and his method was used
right down to modern times.

Mystery had been removed. Earth was now within our
grasp. Understanding earth meant we would
ultimately control it. Of course, Columbus wanted
the earth to be smaller, so he deceived himself. He
was no scientist. In a sense, he wanted to conquer
the earth, and so he carved it down to fit himself.
The crowning irony is that he actually succeeded.

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.